The price of Stock A at 9 A.M. Was ​$14.67. Since​ then, the price has been increasing at the rate of ​$0.08 each hour. At noon the price of Stock B was ​$15.17. It begins to decrease at the rate of ​$0.15 each hour. If the two rates​ continue, in how many hours will the prices of the two stocks be the​ same?

Step-by-step explanation:

1 result(s) found

x  

2

−x−3

Step by Step Solution:

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STEP

1

:

Equation at the end of step 1

STEP

2

:

           x3 + 3x2 - 7x - 12

Simplify   ——————————————————

                 x + 4        

Checking for a perfect cube :

2.1    x3 + 3x2 - 7x - 12  is not a perfect cube

Trying to factor by pulling out :

2.2      Factoring:  x3 + 3x2 - 7x - 12  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  -7x - 12  

Group 2:  x3 + 3x2  

Pull out from each group separately :

Group 1:   (7x + 12) • (-1)

Group 2:   (x + 3) • (x2)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

2.3    Find roots (zeroes) of :       F(x) = x3 + 3x2 - 7x - 12

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -12.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,3 ,4 ,6 ,12

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -3.00      

     -2       1        -2.00        6.00      

     -3       1        -3.00        9.00      

     -4       1        -4.00        0.00      x + 4  

     -6       1        -6.00        -78.00      

     -12       1       -12.00       -1224.00      

     1       1        1.00        -15.00      

     2       1        2.00        -6.00      

     3       1        3.00        21.00      

     4       1        4.00        72.00      

     6       1        6.00        270.00      

     12       1        12.00        2064.00      

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms

In our case this means that

  x3 + 3x2 - 7x - 12  

can be divided with  x + 4  

Polynomial Long Division :

2.4    Polynomial Long Division

Dividing :  x3 + 3x2 - 7x - 12  

                             ("Dividend")

By         :    x + 4    ("Divisor")

dividend     x3  +  3x2  -  7x  -  12  

- divisor  * x2     x3  +  4x2          

remainder      -  x2  -  7x  -  12  

- divisor  * -x1      -  x2  -  4x      

remainder          -  3x  -  12  

- divisor  * -3x0          -  3x  -  12  

remainder                0

Quotient :  x2-x-3  Remainder:  0  

Trying to factor by splitting the middle term

2.5     Factoring  x2-x-3  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -x  its coefficient is  -1 .

The last term, "the constant", is  -3  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -3 = -3  

Step-2 : Find two factors of  -3  whose sum equals the coefficient of the middle term, which is   -1 .

     -3    +    1    =    -2  

     -1    +    3    =    2  

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Canceling Out :

2.6    Cancel out  (x+4)  which appears on both sides of the fraction line.

Final result :

 x2 - x - 3

Terms and topics

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Polynomial root calculator

Polynomial long division

Related links

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Root Finder -- Polynomials Calculator

How to factor five term polynomial - Yahoo Answers

Long Polynomial Division

Polynomial long division - Wikipedia

Polynomial Long Division

Polynomials - Long Division

Step-by-step explanation:

20n 20394848484848575

The impulse on the body is 20 kg-m/s, the final speed of the body is 2m/s, and the distance covered within the time interval is 0.5m.

Force is the strength applied on an object with mass to change its state of motion.

The mass of the body is 10kg.

The force applied on the object is 40N.

The time for which the force is applied is 0.5 sec.

The impulse on the body is calculated by,

Impulse =  Force * Time

Impulse = 40 * 0.5

Impulse = 20 kg-m/s

The final speed of the body is given by

v = u + at

Assuming the initial speed = 0

v = at

Acceleration =  Force / mass

Acceleration = 40/10

a = 4 m/s²

v = 4 * 0.5

v = 2 m/s

The distance covered within the time interval is given by,

s = ut + (1/2) at²

s = (1/2) at²

s = (1/2) 4 * 0.5 *0.5

s = 0.5 m

To know more about Force

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Answer:

d) 0.712

Step-by-step explanation:

Your question isn't clear, so my answer may be wromg

Answer:

(-5, 0.5)

Step-by-step explanation:

-12+2/2= -5

-9+10/2= 0.5

(-5, 0.5)

Answer:

The polynomials can be identified by noting which expressions contain only the operations of addition, subtraction, multiplication, and non-negative integer exponents. The non-polynomial expressions will be the expressions which contain other operations. Explain why the non-polynomial expressions are not polynomials.

Answer:

half a cup

Step-by-step explanation:

if one fourth is needed for 17 and thirty four is the double of 17, then

1/4 x 2 = 2/4

2/4 simplified is 1/2->half

Answer:

15

Step-by-step explanation:

f(x) = 3x -12 for x = 9

f(9) = 3(9) -12

27-12

15

Answer:

-10 + (-7)= -17

Step-by-step explanation:

Answer:

-17

Step-by-step explanation:

-10 plus -7 is -17

Answer:

Step-by-step explanation:

Given Shana temperature = -20°C

°If Pearls temperature is opposite that of Shana's then Pearls temparature = -(-20) = 20°C

Hence the correct way to represent "the opposite of Shana's temperature is equal to Pearl's

Opposite of shana = -(-20°C)

Pearls temperature = +20°C

Since Opposite of shana = Pearls temperature, hence  -(-20°C) = 20°C

Answer:

-(-20 = 20

Step-by-step explanation:

The "opposite" here means we take the negative of -20 C.

So we can write -(-20 which is equal to 20.

So the first option is correct, -(-20 = 20.

hope this helps:)

Answer:

23

Step-by-step explanation:

7-5(1)+3(7)

7-5+21

2+21

23

Answer:

7-5+21 = 23

Step-by-step explanation:

7 - 5p+ 3q

7 - 5(1) + 3(7)

7 - 5 + 21

7 + 16

= 23 hope this helps :)

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Monthly Payment (PMT) = 200 at the end of each period

interest rate = 2.9% = 0.029/12 = 0.0024166

Period (n) = 43 years x 12 = 516

Using the future value(FV) of an ordinary annuity:

FV = PMT[(1 + r)^n - 1] / r

FV = 200[(1 + 0.0024166)^516 - 1] / 0.0024166

FV = 200[(1.0024166)^516 - 1] / 0.0024166

FV = 200(2.4745372) / 0.0024166

FV = 204,794.93

Amount which will be in saving plan towards retirement = $204,794.93

Interest amount :

$204,794.93 - total monthly deposits

$204,794.93 - (200 * 516)

$204,794.93 - $103,200

= $101,594.93

Answer:

The triangles are lined up with their correct pairs already.

Step-by-step explanation:

The leg that is the base is always seen as the bottom, and the leg to the side of it that makes the right angle will always be the height. Though if the base is at the hypotenuse as it is seen in the last photo, the height will be from the point of which the two legs of the triangle meet down to the hypotenuse.

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation: (sorry you'll have to graph them on your own)

Number 2:

So if x was this y would be...

x=-3        y=4            (-3,4)

x=0         y=2            (0,2)

x=3         y=0            (3,0)

The solution would be (3,0).                                                                                

Number 3:

So before we begin we'd have to solve for y by subtracting 1 from both sides to get...        [tex]y=3x-1[/tex]

Now we should choose -1, 0, and 1 so now...

x=-1         y=-4           (-3,4)

x=0         y=-1            (0,2)

x=1          y=2            (3,0)

The solution would be (1,2).                                                                                  

Answer:

The domain of the graph is (-infinity, infinity)

The range of the graph is [0, infinity)

Please mark as helpful if this is helpful!

Thanks

Answer:

x=0

Step-by-step explanation:

Regroup terms:

3x=0

Divide both sides by 3:

3x divided by 3 = x

0 divided by 3 = 0

x=0

Answer:

8

Step-by-step explanation:

4x4=16x8=128

Answer:

The least number of plates and cups she can buy is 24

She will buy 3 packs of plates

She will buy 2 packs of cup

Step-by-step explanation:

Plates = 8 per pack

Cups = 12 per pack

Find the Lowest common multiple of 8 and 12

8 = 16, 24, 32, 40, 48, 56, 64, 72, 80

12 = 24, 36, 48, 60, 72

What is the least number of plates and cups she can buy?

The Lowest common multiple of 8 and 12 is 24

The least number of plates and cups she can buy is 24

How many packs of plates?

Packs of plates = 24 plates / 8 per pack

= 3 packs

She will buy 3 packs of plates

How many packs of cups?

Packs of cups = 24 / 12 per pack

= 2 packs

She will buy 2 packs of cup

Answer:

A

Step-by-step explanation:

Answer:

5 divided by 5/6=6

Answer:

2 1/2 ounces

Step-by-step explanation:

If each coin is 5/6 ounces and she picks up 3, we must multiply the two numbers

5/6 × 3

3 can also be written as 3/1

5/6 × 3/1

multiply the numerators and denominators separately

5 × 3/6 × 1

15/6

Both 15 and 6 have a common factor of 3 so divide both numbers by 3

15 ÷ 3/6 ÷ 3

5/2

This is simplest form in terms of improper fractions

If you want it as a whole number it would be:

2 1/2

This is because 2 goes into 5 twice evenly (whole number) with one remaining (numerator; denominator stays the same)

Hello

Answer:

2.5 ounce

Step-by-step explanation:

Weight of each coin=5/6 ounce

Weight of 3 such coins= 3*5/6

                                     = 2.5 ounces

Hope its in the simplest form....

Answer:

X = 4 and Y = 5

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

We'll have to use trigonometry for this.

First, note that in right triangle ABC, if we look from the perspective of angle A, the opposite side is x, the adjacent side is y, and the hypotenuse is 18.

In order to find x, then, we must use sine, which is opposite/hypotenuse. So:

sin(A) = sin(60) = opposite/hypotenuse = x/18

sin(60) is equal to (√3)/2, so multiplying both sides by 18 gives:

[(√3)/2] * 18 = 9√3

Already, we can tell that the answer is likely C, but let's find y to make sure.

We will use cosine to find y because cos = adjacent/hypotenuse.

cos(A) = cos(60) = adjacent/hypotenuse = y/18

cos(60) = 0.5, so multiplying both sides by 18 gives:

0.5 * 18 = 9

So, y = 9.

Thus, C is our answer.

~ an aesthetics lover

Answer:

C

Step-by-step explanation:

Using the cosine/ sine ratio in the right triangle and the exact values

cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] and sin30° = [tex]\frac{1}{2}[/tex] , then

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{x}{18}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2x = 18[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 9[tex]\sqrt{3}[/tex]

----------------------------------------------------------

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{y}{18}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2y = 18 ( divide both sides by 2 )

y = 9

Thus

x = 9[tex]\sqrt{3}[/tex] and y = 9 → C

Answer:

ok I did this construction about a year ago but I think I can remember something so if it's not correct I hope you won't be mad with me ok so the first step draw a straight line measure the length then make an AC on both sides then stand on one side make an arc upstand on the other side make an arc upthen stand on one AC and make another ARK on top of the other one then stand on the other AC and make another ark on top of the other one then join the lines yeah I think that's the procedure

Answer:

(18 + 36 + 27) = 9 x (2+4+3)

(88 + 66 + 22) = 22 x (4+3+1)

(36 + 96 + 12) = 12 x (3+8+1)

(126 + 28 + 14) = 14 x (9+2+1)

(54 + 81 + 27) = 27 x (2+3+1)

(16 + 28 + 48) = 4 x (4+7+12)

Step-by-step explanation:

The equations in the solution represent each expression as a multiple of a sum of whole numbers with no common factor.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

As per the given question, the required solution would be as:

(18 + 36 + 27) = 9 × (2+4+3)

This equation represents each expression as a multiple of a sum of whole numbers with no common factor.

Similarly further equations like as :

(88 + 66 + 22) = 22 × (4+3+1)

(36 + 96 + 12) = 12 × (3+8+1)

(126 + 28 + 14) = 14 × (9+2+1)

(54 + 81 + 27) = 27 × (2+3+1)

(16 + 28 + 48) = 4 × (4+7+12)

Thus, the above equations represent each expression as a multiple of a sum of whole numbers with no common factor.

Learn more about the algebraic expression here :

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Answer:

A. y = (x - 3)(x + 8)(x - 1)

Step-by-step explanation:

To find zeros of a polynomial, we set the polynomial equal to zero.

We can eliminate C and D; as we set them equal to 0, we see that a root would be 0 due to x. Since we are not looking for a root of 0, those 2 answer choices are incorrect.

Between A and B, A is correct:

A

0 = (x - 3)(x + 8)(x - 1)

x = -8, 1, 3

B

0 = (x + 1)(x - 8)(x + 3)

x = -3, -1, 8

Answer:

Answer A is the correct one.

Step-by-step explanation:

Which function has zeros of -8,1 and 3?  We convert each of these zeros into factors, as follows:  (x + 8), (x - 1), (x - 3).  Answer A is the correct one.

Answer:

Communitive

Step-by-step explanation:

It is just saying that they are congruent and they just restated in different ways. It is like 4+3=7 and 3+4=7

Hope this helps

Answer:

D.

Step-by-step explanation:

SORRY IF THIS IS WRONG IM NOT GOOD IN MATH BUT I TRY

Answer:

The answer is 10^24kg. 0.07346.